Related papers: Groups of Circle Diffeomorphisms

We are raising questions on discrete and dense subgroups of Diff(I). Most of the questions are around the problems discussed in [A1]-[A4].

In the present paper we describe the action of (not necessarily line) bundles of finite order on the $K$-functor in terms of classifying spaces. This description might provide with an approach for more general twistings in $K$-theory than…

Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

We survey new results on finite groups of birational transformations of algebraic varieties.

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on the model theory of these structures.

We build a faithful action of Higman's group on the line by homeomorphisms, answering a question of Yves de Cornulier. As a by-product we obtain many quasimorphisms from the Higman group into the reals. We also show that every action by…

Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

The goal of this paper is to describe all local diffeomorphisms mapping a family of circles, in an open subset of $\r^3$, into straight lines. This paper contains two main results. The first is a complete description of the rectifiable…

The cyclic sieving phenomenon is a well-studied occurrence in combinatorics appearing when a cyclic group acts on a finite set. In this paper, we demonstrate a natural extension of this theory to finite abelian groups. We also present a…

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…

In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.

This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

Conformal fields are a new class of $Vect(N)$ modules which are more general than tensor fields. The corresponding diffeomorphism group action is constructed. Conformal fields are thus invariantly defined.

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of…

This document is a collection of comments that I wrote down while reading the first four chapters of the book "Discrete Groups, Expanding Graphs and Invariant Measures" by Alexander Lubotzky. Most of them are more detailed versions of…